Faculty and factors with recursion

Question

I'm trying to implement the recursion in a slightly different way, but I'm stumped as to the implementation of said math.

Here's my code:

#include <iostream>
using namespace std;



template <const int n>
class faculty
{
public:
    static const int val = faculty<n - 1>::val * n; //Recursion!!!!
};


//For when 1!, return value of 1!
template <>
class faculty<1>
{
public:
    static const int val = 1;
};


//Falling Factorial
template <const int n, const int k>
class fallingcfactorial
{
public:
    static const int n_k = faculty<n>::val / faculty<n - k>::val;
    // (n * n - 1 * ... * 1) / ((n - k) * (n - k + 1) * ... * 1)
};



// Implementing the Factorial a different way
// (n * (n - 1) * ... * (n - k + 1))


//For when n = k then output = 1
template <const int n>
class fallingcfactorial<n, n>
{
public:
    static const int n_k = 1;

};


int main(void) {
    cout << "Faculty of 5 (1*2*3*4*5): " << faculty<5>::val << endl;
    cout << "n(10)_k(5) = " << fallingcfactorial<10, 5>::n_k << endl;
}

Trying to do it (n * (n - 1) * ... * (n - k + 1)) way, I fail at implementing it in code. Math isn't my absolute strong suit, but I do ok.

Answer 1

The use of templates it a little bit tricky. I think this should solve your problem:

#include <iostream>
using namespace std;

template <const int n, const int k>
class fallingFactorial
{
public:
    static const int n_k = fallingFactorial<n - 1, k>::n_k * n;
};

template <const int n>
class fallingFactorial<n, n>
{
public:
    static const int n_k = 1;
};

int main(void) {
    cout << fallingFactorial<10, 5>::n_k << endl;
    return 0;
}

This example is based on partial template specialization (template <const int n> class fallingFactorial<n, n>). When a template class is called the best matching and "most specialized" template is used. Some older compilers doesn't support partial specialization well (see wiki).